#1**+1 **

How can i find the end behavior with these two functions?

\(f(x)=\frac{-6x}{3x-5}\\ f(x)=x^2-4x-5\)

\(\frac{-6x}{3x-5}=x^2-4x-5 \)

\(-6x=(x^2-4x-5)\times (3x-5)\\ -6x=3x^3-5x^2-12x^2+20x-15x+25\\ \color{blue}3x^3-17x^2+11x+25=0\)

\(x_1 \approx-.88231\\ x_2\approx 2.1443\\ x_3 \approx 4.4041\\ WOLFRAM\ |\ ALPHA\)

!

asinus
Oct 3, 2017

#2**+1 **

Mmm I do not think that is what the guest wanted asinus :)

\(f(x)=\frac{-6x}{3x-5}\)

This has an asymptote at

3x-5=0

x=5/3

lim as x tends to 5/3 from above = - infinity

lim as x tends to 5/3 from below = + infinity

As x tends to +infinity y tends to -2

As x tends to -infinity y tends to -2

Here is the graph.

Melody
Oct 3, 2017